Question

If line AD is a tangent to circle B at point C, and m ABC = 55°, what is the measure of BAD?

Answer 1

145°

Explanation:

There are a couple of ways you can get there:

1. ∠ACB is a right angle, 90°. Hence, ∠BAC is the complement of ∠ABC, so is ...

... ∠BAC = 90° -∠ABC = 90° -55° = 35°

Then, ∠BAC and ∠BAD are a linear pair, so total 180°. That makes ∠BAD the supplement of ∠BAC, so ...

... ∠BAD = 180° -35° = 145°

2. ∠BAD is the exterior angle at A for the triangle ABC. It will have a measure that is the sum of the opposite interior angles: given ∠ABC = 55° and right angle ACB = 90°.

... ∠BAD = 55° +90° = 145°